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<h1 align="center">Source for file SingularValueDecomposition.php</h1>
<p>Documentation is available at <a href="../JAMA/_PHPExcel---Shared---JAMA---SingularValueDecomposition.php.html">SingularValueDecomposition.php</a></p>
<div class="src-code">
<ol><li><div class="src-line"><a name="a1"></a><span class="src-php">&lt;?php</span></div></li>
<li><div class="src-line"><a name="a2"></a><span class="src-doc">/**</span></div></li>
<li><div class="src-line"><a name="a3"></a><span class="src-doc">&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;</span><span class="src-doc-coretag">@package</span><span class="src-doc">&nbsp;JAMA</span></div></li>
<li><div class="src-line"><a name="a4"></a><span class="src-doc">&nbsp;*</span></div></li>
<li><div class="src-line"><a name="a5"></a><span class="src-doc">&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;For&nbsp;an&nbsp;m-by-n&nbsp;matrix&nbsp;A&nbsp;with&nbsp;m&nbsp;&gt;=&nbsp;n,&nbsp;the&nbsp;singular&nbsp;value&nbsp;decomposition&nbsp;is</span></div></li>
<li><div class="src-line"><a name="a6"></a><span class="src-doc">&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;an&nbsp;m-by-n&nbsp;orthogonal&nbsp;matrix&nbsp;U,&nbsp;an&nbsp;n-by-n&nbsp;diagonal&nbsp;matrix&nbsp;S,&nbsp;and</span></div></li>
<li><div class="src-line"><a name="a7"></a><span class="src-doc">&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;an&nbsp;n-by-n&nbsp;orthogonal&nbsp;matrix&nbsp;V&nbsp;so&nbsp;that&nbsp;A&nbsp;=&nbsp;U*S*V'.</span></div></li>
<li><div class="src-line"><a name="a8"></a><span class="src-doc">&nbsp;*</span></div></li>
<li><div class="src-line"><a name="a9"></a><span class="src-doc">&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;The&nbsp;singular&nbsp;values,&nbsp;sigma[$k]&nbsp;=&nbsp;S[$k][$k],&nbsp;are&nbsp;ordered&nbsp;so&nbsp;that</span></div></li>
<li><div class="src-line"><a name="a10"></a><span class="src-doc">&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;sigma[0]&nbsp;&gt;=&nbsp;sigma[1]&nbsp;&gt;=&nbsp;...&nbsp;&gt;=&nbsp;sigma[n-1].</span></div></li>
<li><div class="src-line"><a name="a11"></a><span class="src-doc">&nbsp;*</span></div></li>
<li><div class="src-line"><a name="a12"></a><span class="src-doc">&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;The&nbsp;singular&nbsp;value&nbsp;decompostion&nbsp;always&nbsp;exists,&nbsp;so&nbsp;the&nbsp;constructor&nbsp;will</span></div></li>
<li><div class="src-line"><a name="a13"></a><span class="src-doc">&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;never&nbsp;fail.&nbsp;&nbsp;The&nbsp;matrix&nbsp;condition&nbsp;number&nbsp;and&nbsp;the&nbsp;effective&nbsp;numerical</span></div></li>
<li><div class="src-line"><a name="a14"></a><span class="src-doc">&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;rank&nbsp;can&nbsp;be&nbsp;computed&nbsp;from&nbsp;this&nbsp;decomposition.</span></div></li>
<li><div class="src-line"><a name="a15"></a><span class="src-doc">&nbsp;*</span></div></li>
<li><div class="src-line"><a name="a16"></a><span class="src-doc">&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;</span><span class="src-doc-coretag">@author</span><span class="src-doc">&nbsp;&nbsp;Paul&nbsp;Meagher</span></div></li>
<li><div class="src-line"><a name="a17"></a><span class="src-doc">&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;</span><span class="src-doc-coretag">@license</span><span class="src-doc">&nbsp;PHP&nbsp;v3.0</span></div></li>
<li><div class="src-line"><a name="a18"></a><span class="src-doc">&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;</span><span class="src-doc-coretag">@version</span><span class="src-doc">&nbsp;1.1</span></div></li>
<li><div class="src-line"><a name="a19"></a><span class="src-doc">&nbsp;*/</span></div></li>
<li><div class="src-line"><a name="a20"></a><span class="src-key">class&nbsp;</span><a href="../JAMA/SingularValueDecomposition.html">SingularValueDecomposition</a>&nbsp;&nbsp;<span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a21"></a>&nbsp;</div></li>
<li><div class="src-line"><a name="a22"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-doc">/**</span></div></li>
<li><div class="src-line"><a name="a23"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;Internal&nbsp;storage&nbsp;of&nbsp;U.</span></div></li>
<li><div class="src-line"><a name="a24"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;</span><span class="src-doc-coretag">@var&nbsp;</span><span class="src-doc-type">array&nbsp;</span></div></li>
<li><div class="src-line"><a name="a25"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*/</span></div></li>
<li><div class="src-line"><a name="a26"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">private&nbsp;</span><span class="src-var">$U&nbsp;</span>=&nbsp;<span class="src-key">array</span><span class="src-sym">(</span><span class="src-sym">)</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a27"></a>&nbsp;</div></li>
<li><div class="src-line"><a name="a28"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-doc">/**</span></div></li>
<li><div class="src-line"><a name="a29"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;Internal&nbsp;storage&nbsp;of&nbsp;V.</span></div></li>
<li><div class="src-line"><a name="a30"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;</span><span class="src-doc-coretag">@var&nbsp;</span><span class="src-doc-type">array&nbsp;</span></div></li>
<li><div class="src-line"><a name="a31"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*/</span></div></li>
<li><div class="src-line"><a name="a32"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">private&nbsp;</span><span class="src-var">$V&nbsp;</span>=&nbsp;<span class="src-key">array</span><span class="src-sym">(</span><span class="src-sym">)</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a33"></a>&nbsp;</div></li>
<li><div class="src-line"><a name="a34"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-doc">/**</span></div></li>
<li><div class="src-line"><a name="a35"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;Internal&nbsp;storage&nbsp;of&nbsp;singular&nbsp;values.</span></div></li>
<li><div class="src-line"><a name="a36"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;</span><span class="src-doc-coretag">@var&nbsp;</span><span class="src-doc-type">array&nbsp;</span></div></li>
<li><div class="src-line"><a name="a37"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*/</span></div></li>
<li><div class="src-line"><a name="a38"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">private&nbsp;</span><span class="src-var">$s&nbsp;</span>=&nbsp;<span class="src-key">array</span><span class="src-sym">(</span><span class="src-sym">)</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a39"></a>&nbsp;</div></li>
<li><div class="src-line"><a name="a40"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-doc">/**</span></div></li>
<li><div class="src-line"><a name="a41"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;Row&nbsp;dimension.</span></div></li>
<li><div class="src-line"><a name="a42"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;</span><span class="src-doc-coretag">@var&nbsp;</span><span class="src-doc-type">int&nbsp;</span></div></li>
<li><div class="src-line"><a name="a43"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*/</span></div></li>
<li><div class="src-line"><a name="a44"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">private&nbsp;</span><span class="src-var">$m</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a45"></a>&nbsp;</div></li>
<li><div class="src-line"><a name="a46"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-doc">/**</span></div></li>
<li><div class="src-line"><a name="a47"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;Column&nbsp;dimension.</span></div></li>
<li><div class="src-line"><a name="a48"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;</span><span class="src-doc-coretag">@var&nbsp;</span><span class="src-doc-type">int&nbsp;</span></div></li>
<li><div class="src-line"><a name="a49"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*/</span></div></li>
<li><div class="src-line"><a name="a50"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">private&nbsp;</span><span class="src-var">$n</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a51"></a>&nbsp;</div></li>
<li><div class="src-line"><a name="a52"></a>&nbsp;</div></li>
<li><div class="src-line"><a name="a53"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-doc">/**</span></div></li>
<li><div class="src-line"><a name="a54"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;Construct&nbsp;the&nbsp;singular&nbsp;value&nbsp;decomposition</span></div></li>
<li><div class="src-line"><a name="a55"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*</span></div></li>
<li><div class="src-line"><a name="a56"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;Derived&nbsp;from&nbsp;LINPACK&nbsp;code.</span></div></li>
<li><div class="src-line"><a name="a57"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*</span></div></li>
<li><div class="src-line"><a name="a58"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;</span><span class="src-doc-coretag">@param&nbsp;</span><span class="src-doc-type">$A&nbsp;</span><span class="src-doc">Rectangular&nbsp;matrix</span></div></li>
<li><div class="src-line"><a name="a59"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;</span><span class="src-doc-coretag">@return&nbsp;</span><span class="src-doc-type">Structure&nbsp;</span><span class="src-doc">to&nbsp;access&nbsp;U,&nbsp;S&nbsp;and&nbsp;V.</span></div></li>
<li><div class="src-line"><a name="a60"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*/</span></div></li>
<li><div class="src-line"><a name="a61"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">public&nbsp;</span><span class="src-key">function&nbsp;</span><a href="../JAMA/SingularValueDecomposition.html#method__construct">__construct</a><span class="src-sym">(</span><span class="src-var">$Arg</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a62"></a>&nbsp;</div></li>
<li><div class="src-line"><a name="a63"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;Initialize.</span></div></li>
<li><div class="src-line"><a name="a64"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$A&nbsp;</span>=&nbsp;<span class="src-var">$Arg</span><span class="src-sym">-&gt;</span><span class="src-id">getArrayCopy</span><span class="src-sym">(</span><span class="src-sym">)</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a65"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">m&nbsp;</span>=&nbsp;<span class="src-var">$Arg</span><span class="src-sym">-&gt;</span><span class="src-id">getRowDimension</span><span class="src-sym">(</span><span class="src-sym">)</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a66"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">n&nbsp;</span>=&nbsp;<span class="src-var">$Arg</span><span class="src-sym">-&gt;</span><span class="src-id">getColumnDimension</span><span class="src-sym">(</span><span class="src-sym">)</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a67"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$nu&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</span>=&nbsp;<a href="http://www.php.net/min">min</a><span class="src-sym">(</span><span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">m</span><span class="src-sym">,&nbsp;</span><span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">n</span><span class="src-sym">)</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a68"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$e&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</span>=&nbsp;<span class="src-key">array</span><span class="src-sym">(</span><span class="src-sym">)</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a69"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$work&nbsp;&nbsp;&nbsp;&nbsp;</span>=&nbsp;<span class="src-key">array</span><span class="src-sym">(</span><span class="src-sym">)</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a70"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$wantu&nbsp;&nbsp;&nbsp;</span>=&nbsp;<span class="src-id">true</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a71"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$wantv&nbsp;&nbsp;&nbsp;</span>=&nbsp;<span class="src-id">true</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a72"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$nct&nbsp;</span>=&nbsp;<a href="http://www.php.net/min">min</a><span class="src-sym">(</span><span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">m&nbsp;</span>-&nbsp;<span class="src-num">1</span><span class="src-sym">,&nbsp;</span><span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">n</span><span class="src-sym">)</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a73"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$nrt&nbsp;</span>=&nbsp;<a href="http://www.php.net/max">max</a><span class="src-sym">(</span><span class="src-num">0</span><span class="src-sym">,&nbsp;</span><a href="http://www.php.net/min">min</a><span class="src-sym">(</span><span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">n&nbsp;</span>-&nbsp;<span class="src-num">2</span><span class="src-sym">,&nbsp;</span><span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">m</span><span class="src-sym">))</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a74"></a>&nbsp;</div></li>
<li><div class="src-line"><a name="a75"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;Reduce&nbsp;A&nbsp;to&nbsp;bidiagonal&nbsp;form,&nbsp;storing&nbsp;the&nbsp;diagonal&nbsp;elements</span></div></li>
<li><div class="src-line"><a name="a76"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;in&nbsp;s&nbsp;and&nbsp;the&nbsp;super-diagonal&nbsp;elements&nbsp;in&nbsp;e.</span></div></li>
<li><div class="src-line"><a name="a77"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$k&nbsp;</span>=&nbsp;<span class="src-num">0</span><span class="src-sym">;&nbsp;</span><span class="src-var">$k&nbsp;</span>&lt;&nbsp;<a href="http://www.php.net/max">max</a><span class="src-sym">(</span><span class="src-var">$nct</span><span class="src-sym">,</span><span class="src-var">$nrt</span><span class="src-sym">)</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$k</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a78"></a>&nbsp;</div></li>
<li><div class="src-line"><a name="a79"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">if&nbsp;</span><span class="src-sym">(</span><span class="src-var">$k&nbsp;</span>&lt;&nbsp;<span class="src-var">$nct</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a80"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;Compute&nbsp;the&nbsp;transformation&nbsp;for&nbsp;the&nbsp;k-th&nbsp;column&nbsp;and</span></div></li>
<li><div class="src-line"><a name="a81"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;place&nbsp;the&nbsp;k-th&nbsp;diagonal&nbsp;in&nbsp;s[$k].</span></div></li>
<li><div class="src-line"><a name="a82"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;Compute&nbsp;2-norm&nbsp;of&nbsp;k-th&nbsp;column&nbsp;without&nbsp;under/overflow.</span></div></li>
<li><div class="src-line"><a name="a83"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">s</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-num">0</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a84"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$i&nbsp;</span>=&nbsp;<span class="src-var">$k</span><span class="src-sym">;&nbsp;</span><span class="src-var">$i&nbsp;</span>&lt;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">m</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$i</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a85"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">s</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]&nbsp;</span>=&nbsp;<a href="../JAMA/_PHPExcel---Shared---JAMA---utils---Maths.php.html#functionhypo">hypo</a><span class="src-sym">(</span><span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">s</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]</span><span class="src-sym">,&nbsp;</span><span class="src-var">$A</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]</span><span class="src-sym">)</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a86"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a87"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">if&nbsp;</span><span class="src-sym">(</span><span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">s</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]&nbsp;</span>!=&nbsp;<span class="src-num">0.0</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a88"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">if&nbsp;</span><span class="src-sym">(</span><span class="src-var">$A</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]&nbsp;</span>&lt;&nbsp;<span class="src-num">0.0</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a89"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">s</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]&nbsp;</span>=&nbsp;-<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">s</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a90"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a91"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$i&nbsp;</span>=&nbsp;<span class="src-var">$k</span><span class="src-sym">;&nbsp;</span><span class="src-var">$i&nbsp;</span>&lt;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">m</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$i</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a92"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$A</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]&nbsp;</span>/=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">s</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a93"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a94"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$A</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]&nbsp;</span>+=&nbsp;<span class="src-num">1.0</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a95"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a96"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">s</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]&nbsp;</span>=&nbsp;-<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">s</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a97"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a98"></a>&nbsp;</div></li>
<li><div class="src-line"><a name="a99"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$j&nbsp;</span>=&nbsp;<span class="src-var">$k&nbsp;</span>+&nbsp;<span class="src-num">1</span><span class="src-sym">;&nbsp;</span><span class="src-var">$j&nbsp;</span>&lt;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">n</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$j</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a100"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">if&nbsp;</span><span class="src-sym">((</span><span class="src-var">$k&nbsp;</span>&lt;&nbsp;<span class="src-var">$nct</span><span class="src-sym">)&nbsp;</span><span class="src-sym">&amp;&nbsp;</span><span class="src-sym">(</span><span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">s</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]&nbsp;</span>!=&nbsp;<span class="src-num">0.0</span><span class="src-sym">))&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a101"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;Apply&nbsp;the&nbsp;transformation.</span></div></li>
<li><div class="src-line"><a name="a102"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$t&nbsp;</span>=&nbsp;<span class="src-num">0</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a103"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$i&nbsp;</span>=&nbsp;<span class="src-var">$k</span><span class="src-sym">;&nbsp;</span><span class="src-var">$i&nbsp;</span>&lt;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">m</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$i</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a104"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$t&nbsp;</span>+=&nbsp;<span class="src-var">$A</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]&nbsp;</span>*&nbsp;<span class="src-var">$A</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a105"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a106"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$t&nbsp;</span>=&nbsp;-<span class="src-var">$t&nbsp;</span>/&nbsp;<span class="src-var">$A</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a107"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$i&nbsp;</span>=&nbsp;<span class="src-var">$k</span><span class="src-sym">;&nbsp;</span><span class="src-var">$i&nbsp;</span>&lt;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">m</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$i</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a108"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$A</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]&nbsp;</span>+=&nbsp;<span class="src-var">$t&nbsp;</span>*&nbsp;<span class="src-var">$A</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a109"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a110"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;Place&nbsp;the&nbsp;k-th&nbsp;row&nbsp;of&nbsp;A&nbsp;into&nbsp;e&nbsp;for&nbsp;the</span></div></li>
<li><div class="src-line"><a name="a111"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;subsequent&nbsp;calculation&nbsp;of&nbsp;the&nbsp;row&nbsp;transformation.</span></div></li>
<li><div class="src-line"><a name="a112"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$e</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-var">$A</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a113"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a114"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a115"></a>&nbsp;</div></li>
<li><div class="src-line"><a name="a116"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">if&nbsp;</span><span class="src-sym">(</span><span class="src-var">$wantu&nbsp;</span><span class="src-key">AND&nbsp;</span><span class="src-sym">(</span><span class="src-var">$k&nbsp;</span>&lt;&nbsp;<span class="src-var">$nct</span><span class="src-sym">))&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a117"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;Place&nbsp;the&nbsp;transformation&nbsp;in&nbsp;U&nbsp;for&nbsp;subsequent&nbsp;back</span></div></li>
<li><div class="src-line"><a name="a118"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;multiplication.</span></div></li>
<li><div class="src-line"><a name="a119"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$i&nbsp;</span>=&nbsp;<span class="src-var">$k</span><span class="src-sym">;&nbsp;</span><span class="src-var">$i&nbsp;</span>&lt;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">m</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$i</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a120"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">U</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-var">$A</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a121"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a122"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a123"></a>&nbsp;</div></li>
<li><div class="src-line"><a name="a124"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">if&nbsp;</span><span class="src-sym">(</span><span class="src-var">$k&nbsp;</span>&lt;&nbsp;<span class="src-var">$nrt</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a125"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;Compute&nbsp;the&nbsp;k-th&nbsp;row&nbsp;transformation&nbsp;and&nbsp;place&nbsp;the</span></div></li>
<li><div class="src-line"><a name="a126"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;k-th&nbsp;super-diagonal&nbsp;in&nbsp;e[$k].</span></div></li>
<li><div class="src-line"><a name="a127"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;Compute&nbsp;2-norm&nbsp;without&nbsp;under/overflow.</span></div></li>
<li><div class="src-line"><a name="a128"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$e</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-num">0</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a129"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$i&nbsp;</span>=&nbsp;<span class="src-var">$k&nbsp;</span>+&nbsp;<span class="src-num">1</span><span class="src-sym">;&nbsp;</span><span class="src-var">$i&nbsp;</span>&lt;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">n</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$i</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a130"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$e</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]&nbsp;</span>=&nbsp;<a href="../JAMA/_PHPExcel---Shared---JAMA---utils---Maths.php.html#functionhypo">hypo</a><span class="src-sym">(</span><span class="src-var">$e</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]</span><span class="src-sym">,&nbsp;</span><span class="src-var">$e</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">)</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a131"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a132"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">if&nbsp;</span><span class="src-sym">(</span><span class="src-var">$e</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]&nbsp;</span>!=&nbsp;<span class="src-num">0.0</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a133"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">if&nbsp;</span><span class="src-sym">(</span><span class="src-var">$e</span><span class="src-sym">[</span><span class="src-var">$k</span>+<span class="src-num">1</span><span class="src-sym">]&nbsp;</span>&lt;&nbsp;<span class="src-num">0.0</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a134"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$e</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]&nbsp;</span>=&nbsp;-<span class="src-var">$e</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a135"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a136"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$i&nbsp;</span>=&nbsp;<span class="src-var">$k&nbsp;</span>+&nbsp;<span class="src-num">1</span><span class="src-sym">;&nbsp;</span><span class="src-var">$i&nbsp;</span>&lt;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">n</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$i</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a137"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$e</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]&nbsp;</span>/=&nbsp;<span class="src-var">$e</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a138"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a139"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$e</span><span class="src-sym">[</span><span class="src-var">$k</span>+<span class="src-num">1</span><span class="src-sym">]&nbsp;</span>+=&nbsp;<span class="src-num">1.0</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a140"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a141"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$e</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]&nbsp;</span>=&nbsp;-<span class="src-var">$e</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a142"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">if&nbsp;</span><span class="src-sym">((</span><span class="src-var">$k</span>+<span class="src-num">1&nbsp;</span>&lt;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">m</span><span class="src-sym">)&nbsp;</span><span class="src-key">AND&nbsp;</span><span class="src-sym">(</span><span class="src-var">$e</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]&nbsp;</span>!=&nbsp;<span class="src-num">0.0</span><span class="src-sym">))&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a143"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;Apply&nbsp;the&nbsp;transformation.</span></div></li>
<li><div class="src-line"><a name="a144"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$i&nbsp;</span>=&nbsp;<span class="src-var">$k</span>+<span class="src-num">1</span><span class="src-sym">;&nbsp;</span><span class="src-var">$i&nbsp;</span>&lt;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">m</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$i</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a145"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$work</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-num">0.0</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a146"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a147"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$j&nbsp;</span>=&nbsp;<span class="src-var">$k</span>+<span class="src-num">1</span><span class="src-sym">;&nbsp;</span><span class="src-var">$j&nbsp;</span>&lt;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">n</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$j</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a148"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$i&nbsp;</span>=&nbsp;<span class="src-var">$k</span>+<span class="src-num">1</span><span class="src-sym">;&nbsp;</span><span class="src-var">$i&nbsp;</span>&lt;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">m</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$i</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a149"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$work</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]&nbsp;</span>+=&nbsp;<span class="src-var">$e</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]&nbsp;</span>*&nbsp;<span class="src-var">$A</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a150"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a151"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a152"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$j&nbsp;</span>=&nbsp;<span class="src-var">$k&nbsp;</span>+&nbsp;<span class="src-num">1</span><span class="src-sym">;&nbsp;</span><span class="src-var">$j&nbsp;</span>&lt;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">n</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$j</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a153"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$t&nbsp;</span>=&nbsp;-<span class="src-var">$e</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]&nbsp;</span>/&nbsp;<span class="src-var">$e</span><span class="src-sym">[</span><span class="src-var">$k</span>+<span class="src-num">1</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a154"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$i&nbsp;</span>=&nbsp;<span class="src-var">$k&nbsp;</span>+&nbsp;<span class="src-num">1</span><span class="src-sym">;&nbsp;</span><span class="src-var">$i&nbsp;</span>&lt;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">m</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$i</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a155"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$A</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]&nbsp;</span>+=&nbsp;<span class="src-var">$t&nbsp;</span>*&nbsp;<span class="src-var">$work</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a156"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a157"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a158"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a159"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">if&nbsp;</span><span class="src-sym">(</span><span class="src-var">$wantv</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a160"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;Place&nbsp;the&nbsp;transformation&nbsp;in&nbsp;V&nbsp;for&nbsp;subsequent</span></div></li>
<li><div class="src-line"><a name="a161"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;back&nbsp;multiplication.</span></div></li>
<li><div class="src-line"><a name="a162"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$i&nbsp;</span>=&nbsp;<span class="src-var">$k&nbsp;</span>+&nbsp;<span class="src-num">1</span><span class="src-sym">;&nbsp;</span><span class="src-var">$i&nbsp;</span>&lt;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">n</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$i</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a163"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">V</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-var">$e</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a164"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a165"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a166"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a167"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a168"></a>&nbsp;</div></li>
<li><div class="src-line"><a name="a169"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;Set&nbsp;up&nbsp;the&nbsp;final&nbsp;bidiagonal&nbsp;matrix&nbsp;or&nbsp;order&nbsp;p.</span></div></li>
<li><div class="src-line"><a name="a170"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$p&nbsp;</span>=&nbsp;<a href="http://www.php.net/min">min</a><span class="src-sym">(</span><span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">n</span><span class="src-sym">,&nbsp;</span><span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">m&nbsp;</span>+&nbsp;<span class="src-num">1</span><span class="src-sym">)</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a171"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">if&nbsp;</span><span class="src-sym">(</span><span class="src-var">$nct&nbsp;</span>&lt;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">n</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a172"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">s</span><span class="src-sym">[</span><span class="src-var">$nct</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-var">$A</span><span class="src-sym">[</span><span class="src-var">$nct</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$nct</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a173"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a174"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">if&nbsp;</span><span class="src-sym">(</span><span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">m&nbsp;</span>&lt;&nbsp;<span class="src-var">$p</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a175"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">s</span><span class="src-sym">[</span><span class="src-var">$p</span>-<span class="src-num">1</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-num">0.0</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a176"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a177"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">if&nbsp;</span><span class="src-sym">(</span><span class="src-var">$nrt&nbsp;</span>+&nbsp;<span class="src-num">1&nbsp;</span>&lt;&nbsp;<span class="src-var">$p</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a178"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$e</span><span class="src-sym">[</span><span class="src-var">$nrt</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-var">$A</span><span class="src-sym">[</span><span class="src-var">$nrt</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$p</span>-<span class="src-num">1</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a179"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a180"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$e</span><span class="src-sym">[</span><span class="src-var">$p</span>-<span class="src-num">1</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-num">0.0</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a181"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;If&nbsp;required,&nbsp;generate&nbsp;U.</span></div></li>
<li><div class="src-line"><a name="a182"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">if&nbsp;</span><span class="src-sym">(</span><span class="src-var">$wantu</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a183"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$j&nbsp;</span>=&nbsp;<span class="src-var">$nct</span><span class="src-sym">;&nbsp;</span><span class="src-var">$j&nbsp;</span>&lt;&nbsp;<span class="src-var">$nu</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$j</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a184"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$i&nbsp;</span>=&nbsp;<span class="src-num">0</span><span class="src-sym">;&nbsp;</span><span class="src-var">$i&nbsp;</span>&lt;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">m</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$i</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a185"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">U</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-num">0.0</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a186"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a187"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">U</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-num">1.0</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a188"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a189"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$k&nbsp;</span>=&nbsp;<span class="src-var">$nct&nbsp;</span>-&nbsp;<span class="src-num">1</span><span class="src-sym">;&nbsp;</span><span class="src-var">$k&nbsp;</span>&gt;=&nbsp;<span class="src-num">0</span><span class="src-sym">;&nbsp;</span>--<span class="src-var">$k</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a190"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">if&nbsp;</span><span class="src-sym">(</span><span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">s</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]&nbsp;</span>!=&nbsp;<span class="src-num">0.0</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a191"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$j&nbsp;</span>=&nbsp;<span class="src-var">$k&nbsp;</span>+&nbsp;<span class="src-num">1</span><span class="src-sym">;&nbsp;</span><span class="src-var">$j&nbsp;</span>&lt;&nbsp;<span class="src-var">$nu</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$j</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a192"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$t&nbsp;</span>=&nbsp;<span class="src-num">0</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a193"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$i&nbsp;</span>=&nbsp;<span class="src-var">$k</span><span class="src-sym">;&nbsp;</span><span class="src-var">$i&nbsp;</span>&lt;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">m</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$i</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a194"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$t&nbsp;</span>+=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">U</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]&nbsp;</span>*&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">U</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a195"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a196"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$t&nbsp;</span>=&nbsp;-<span class="src-var">$t&nbsp;</span>/&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">U</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a197"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$i&nbsp;</span>=&nbsp;<span class="src-var">$k</span><span class="src-sym">;&nbsp;</span><span class="src-var">$i&nbsp;</span>&lt;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">m</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$i</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a198"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">U</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]&nbsp;</span>+=&nbsp;<span class="src-var">$t&nbsp;</span>*&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">U</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a199"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a200"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a201"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$i&nbsp;</span>=&nbsp;<span class="src-var">$k</span><span class="src-sym">;&nbsp;</span><span class="src-var">$i&nbsp;</span>&lt;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">m</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$i&nbsp;</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a202"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">U</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]&nbsp;</span>=&nbsp;-<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">U</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a203"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a204"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">U</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-num">1.0&nbsp;</span>+&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">U</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a205"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$i&nbsp;</span>=&nbsp;<span class="src-num">0</span><span class="src-sym">;&nbsp;</span><span class="src-var">$i&nbsp;</span>&lt;&nbsp;<span class="src-var">$k&nbsp;</span>-&nbsp;<span class="src-num">1</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$i</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a206"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">U</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-num">0.0</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a207"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a208"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}&nbsp;</span><span class="src-key">else&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a209"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$i&nbsp;</span>=&nbsp;<span class="src-num">0</span><span class="src-sym">;&nbsp;</span><span class="src-var">$i&nbsp;</span>&lt;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">m</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$i</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a210"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">U</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-num">0.0</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a211"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a212"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">U</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-num">1.0</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a213"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a214"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a215"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a216"></a>&nbsp;</div></li>
<li><div class="src-line"><a name="a217"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;If&nbsp;required,&nbsp;generate&nbsp;V.</span></div></li>
<li><div class="src-line"><a name="a218"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">if&nbsp;</span><span class="src-sym">(</span><span class="src-var">$wantv</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a219"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$k&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">n&nbsp;</span>-&nbsp;<span class="src-num">1</span><span class="src-sym">;&nbsp;</span><span class="src-var">$k&nbsp;</span>&gt;=&nbsp;<span class="src-num">0</span><span class="src-sym">;&nbsp;</span>--<span class="src-var">$k</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a220"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">if&nbsp;</span><span class="src-sym">((</span><span class="src-var">$k&nbsp;</span>&lt;&nbsp;<span class="src-var">$nrt</span><span class="src-sym">)&nbsp;</span><span class="src-key">AND&nbsp;</span><span class="src-sym">(</span><span class="src-var">$e</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]&nbsp;</span>!=&nbsp;<span class="src-num">0.0</span><span class="src-sym">))&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a221"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$j&nbsp;</span>=&nbsp;<span class="src-var">$k&nbsp;</span>+&nbsp;<span class="src-num">1</span><span class="src-sym">;&nbsp;</span><span class="src-var">$j&nbsp;</span>&lt;&nbsp;<span class="src-var">$nu</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$j</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a222"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$t&nbsp;</span>=&nbsp;<span class="src-num">0</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a223"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$i&nbsp;</span>=&nbsp;<span class="src-var">$k&nbsp;</span>+&nbsp;<span class="src-num">1</span><span class="src-sym">;&nbsp;</span><span class="src-var">$i&nbsp;</span>&lt;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">n</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$i</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a224"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$t&nbsp;</span>+=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">V</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]</span>*&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">V</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a225"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a226"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$t&nbsp;</span>=&nbsp;-<span class="src-var">$t&nbsp;</span>/&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">V</span><span class="src-sym">[</span><span class="src-var">$k</span>+<span class="src-num">1</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a227"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$i&nbsp;</span>=&nbsp;<span class="src-var">$k&nbsp;</span>+&nbsp;<span class="src-num">1</span><span class="src-sym">;&nbsp;</span><span class="src-var">$i&nbsp;</span>&lt;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">n</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$i</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a228"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">V</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]&nbsp;</span>+=&nbsp;<span class="src-var">$t&nbsp;</span>*&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">V</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a229"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a230"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a231"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a232"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$i&nbsp;</span>=&nbsp;<span class="src-num">0</span><span class="src-sym">;&nbsp;</span><span class="src-var">$i&nbsp;</span>&lt;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">n</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$i</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a233"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">V</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-num">0.0</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a234"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a235"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">V</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-num">1.0</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a236"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a237"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a238"></a>&nbsp;</div></li>
<li><div class="src-line"><a name="a239"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;Main&nbsp;iteration&nbsp;loop&nbsp;for&nbsp;the&nbsp;singular&nbsp;values.</span></div></li>
<li><div class="src-line"><a name="a240"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$pp&nbsp;&nbsp;&nbsp;</span>=&nbsp;<span class="src-var">$p&nbsp;</span>-&nbsp;<span class="src-num">1</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a241"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$iter&nbsp;</span>=&nbsp;<span class="src-num">0</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a242"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$eps&nbsp;&nbsp;</span>=&nbsp;<a href="http://www.php.net/pow">pow</a><span class="src-sym">(</span><span class="src-num">2.0</span><span class="src-sym">,&nbsp;</span>-<span class="src-num">52.0</span><span class="src-sym">)</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a243"></a>&nbsp;</div></li>
<li><div class="src-line"><a name="a244"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">while&nbsp;</span><span class="src-sym">(</span><span class="src-var">$p&nbsp;</span>&gt;&nbsp;<span class="src-num">0</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a245"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;Here&nbsp;is&nbsp;where&nbsp;a&nbsp;test&nbsp;for&nbsp;too&nbsp;many&nbsp;iterations&nbsp;would&nbsp;go.</span></div></li>
<li><div class="src-line"><a name="a246"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;This&nbsp;section&nbsp;of&nbsp;the&nbsp;program&nbsp;inspects&nbsp;for&nbsp;negligible</span></div></li>
<li><div class="src-line"><a name="a247"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;elements&nbsp;in&nbsp;the&nbsp;s&nbsp;and&nbsp;e&nbsp;arrays.&nbsp;&nbsp;On&nbsp;completion&nbsp;the</span></div></li>
<li><div class="src-line"><a name="a248"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;variables&nbsp;kase&nbsp;and&nbsp;k&nbsp;are&nbsp;set&nbsp;as&nbsp;follows:</span></div></li>
<li><div class="src-line"><a name="a249"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;kase&nbsp;=&nbsp;1&nbsp;&nbsp;if&nbsp;s(p)&nbsp;and&nbsp;e[k-1]&nbsp;are&nbsp;negligible&nbsp;and&nbsp;k&lt;p</span></div></li>
<li><div class="src-line"><a name="a250"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;kase&nbsp;=&nbsp;2&nbsp;&nbsp;if&nbsp;s(k)&nbsp;is&nbsp;negligible&nbsp;and&nbsp;k&lt;p</span></div></li>
<li><div class="src-line"><a name="a251"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;kase&nbsp;=&nbsp;3&nbsp;&nbsp;if&nbsp;e[k-1]&nbsp;is&nbsp;negligible,&nbsp;k&lt;p,&nbsp;and</span></div></li>
<li><div class="src-line"><a name="a252"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;s(k),&nbsp;...,&nbsp;s(p)&nbsp;are&nbsp;not&nbsp;negligible&nbsp;(qr&nbsp;step).</span></div></li>
<li><div class="src-line"><a name="a253"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;kase&nbsp;=&nbsp;4&nbsp;&nbsp;if&nbsp;e(p-1)&nbsp;is&nbsp;negligible&nbsp;(convergence).</span></div></li>
<li><div class="src-line"><a name="a254"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$k&nbsp;</span>=&nbsp;<span class="src-var">$p&nbsp;</span>-&nbsp;<span class="src-num">2</span><span class="src-sym">;&nbsp;</span><span class="src-var">$k&nbsp;</span>&gt;=&nbsp;-<span class="src-num">1</span><span class="src-sym">;&nbsp;</span>--<span class="src-var">$k</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a255"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">if&nbsp;</span><span class="src-sym">(</span><span class="src-var">$k&nbsp;</span>==&nbsp;-<span class="src-num">1</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a256"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">break</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a257"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a258"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">if&nbsp;</span><span class="src-sym">(</span><a href="http://www.php.net/abs">abs</a><span class="src-sym">(</span><span class="src-var">$e</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]</span><span class="src-sym">)&nbsp;</span>&lt;=&nbsp;<span class="src-var">$eps&nbsp;</span>*&nbsp;<span class="src-sym">(</span><a href="http://www.php.net/abs">abs</a><span class="src-sym">(</span><span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">s</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]</span><span class="src-sym">)&nbsp;</span>+&nbsp;<a href="http://www.php.net/abs">abs</a><span class="src-sym">(</span><span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">s</span><span class="src-sym">[</span><span class="src-var">$k</span>+<span class="src-num">1</span><span class="src-sym">]</span><span class="src-sym">)))&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a259"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$e</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-num">0.0</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a260"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">break</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a261"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a262"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a263"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">if&nbsp;</span><span class="src-sym">(</span><span class="src-var">$k&nbsp;</span>==&nbsp;<span class="src-var">$p&nbsp;</span>-&nbsp;<span class="src-num">2</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a264"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$kase&nbsp;</span>=&nbsp;<span class="src-num">4</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a265"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}&nbsp;</span><span class="src-key">else&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a266"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$ks&nbsp;</span>=&nbsp;<span class="src-var">$p&nbsp;</span>-&nbsp;<span class="src-num">1</span><span class="src-sym">;&nbsp;</span><span class="src-var">$ks&nbsp;</span>&gt;=&nbsp;<span class="src-var">$k</span><span class="src-sym">;&nbsp;</span>--<span class="src-var">$ks</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a267"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">if&nbsp;</span><span class="src-sym">(</span><span class="src-var">$ks&nbsp;</span>==&nbsp;<span class="src-var">$k</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a268"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">break</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a269"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a270"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$t&nbsp;</span>=&nbsp;<span class="src-sym">(</span><span class="src-var">$ks&nbsp;</span>!=&nbsp;<span class="src-var">$p&nbsp;</span>?&nbsp;<a href="http://www.php.net/abs">abs</a><span class="src-sym">(</span><span class="src-var">$e</span><span class="src-sym">[</span><span class="src-var">$ks</span><span class="src-sym">]</span><span class="src-sym">)&nbsp;</span>:&nbsp;<span class="src-num">0.</span><span class="src-sym">)&nbsp;</span>+&nbsp;<span class="src-sym">(</span><span class="src-var">$ks&nbsp;</span>!=&nbsp;<span class="src-var">$k&nbsp;</span>+&nbsp;<span class="src-num">1&nbsp;</span>?&nbsp;<a href="http://www.php.net/abs">abs</a><span class="src-sym">(</span><span class="src-var">$e</span><span class="src-sym">[</span><span class="src-var">$ks</span>-<span class="src-num">1</span><span class="src-sym">]</span><span class="src-sym">)&nbsp;</span>:&nbsp;<span class="src-num">0.</span><span class="src-sym">)</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a271"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">if&nbsp;</span><span class="src-sym">(</span><a href="http://www.php.net/abs">abs</a><span class="src-sym">(</span><span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">s</span><span class="src-sym">[</span><span class="src-var">$ks</span><span class="src-sym">]</span><span class="src-sym">)&nbsp;</span>&lt;=&nbsp;<span class="src-var">$eps&nbsp;</span>*&nbsp;<span class="src-var">$t</span><span class="src-sym">)&nbsp;&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a272"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">s</span><span class="src-sym">[</span><span class="src-var">$ks</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-num">0.0</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a273"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">break</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a274"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a275"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a276"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">if&nbsp;</span><span class="src-sym">(</span><span class="src-var">$ks&nbsp;</span>==&nbsp;<span class="src-var">$k</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a277"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$kase&nbsp;</span>=&nbsp;<span class="src-num">3</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a278"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}&nbsp;</span><span class="src-key">else&nbsp;</span><span class="src-key">if&nbsp;</span><span class="src-sym">(</span><span class="src-var">$ks&nbsp;</span>==&nbsp;<span class="src-var">$p</span>-<span class="src-num">1</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a279"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$kase&nbsp;</span>=&nbsp;<span class="src-num">1</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a280"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}&nbsp;</span><span class="src-key">else&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a281"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$kase&nbsp;</span>=&nbsp;<span class="src-num">2</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a282"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$k&nbsp;</span>=&nbsp;<span class="src-var">$ks</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a283"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a284"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a285"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;++<span class="src-var">$k</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a286"></a>&nbsp;</div></li>
<li><div class="src-line"><a name="a287"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;Perform&nbsp;the&nbsp;task&nbsp;indicated&nbsp;by&nbsp;kase.</span></div></li>
<li><div class="src-line"><a name="a288"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">switch&nbsp;</span><span class="src-sym">(</span><span class="src-var">$kase</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a289"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;Deflate&nbsp;negligible&nbsp;s(p).</span></div></li>
<li><div class="src-line"><a name="a290"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">case&nbsp;</span><span class="src-num">1</span>:</div></li>
<li><div class="src-line"><a name="a291"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$f&nbsp;</span>=&nbsp;<span class="src-var">$e</span><span class="src-sym">[</span><span class="src-var">$p</span>-<span class="src-num">2</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a292"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$e</span><span class="src-sym">[</span><span class="src-var">$p</span>-<span class="src-num">2</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-num">0.0</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a293"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$j&nbsp;</span>=&nbsp;<span class="src-var">$p&nbsp;</span>-&nbsp;<span class="src-num">2</span><span class="src-sym">;&nbsp;</span><span class="src-var">$j&nbsp;</span>&gt;=&nbsp;<span class="src-var">$k</span><span class="src-sym">;&nbsp;</span>--<span class="src-var">$j</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a294"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$t&nbsp;&nbsp;</span>=&nbsp;<a href="../JAMA/_PHPExcel---Shared---JAMA---utils---Maths.php.html#functionhypo">hypo</a><span class="src-sym">(</span><span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">s</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]</span><span class="src-sym">,</span><span class="src-var">$f</span><span class="src-sym">)</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a295"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$cs&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">s</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]&nbsp;</span>/&nbsp;<span class="src-var">$t</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a296"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$sn&nbsp;</span>=&nbsp;<span class="src-var">$f&nbsp;</span>/&nbsp;<span class="src-var">$t</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a297"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">s</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-var">$t</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a298"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">if&nbsp;</span><span class="src-sym">(</span><span class="src-var">$j&nbsp;</span>!=&nbsp;<span class="src-var">$k</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a299"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$f&nbsp;</span>=&nbsp;-<span class="src-var">$sn&nbsp;</span>*&nbsp;<span class="src-var">$e</span><span class="src-sym">[</span><span class="src-var">$j</span>-<span class="src-num">1</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a300"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$e</span><span class="src-sym">[</span><span class="src-var">$j</span>-<span class="src-num">1</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-var">$cs&nbsp;</span>*&nbsp;<span class="src-var">$e</span><span class="src-sym">[</span><span class="src-var">$j</span>-<span class="src-num">1</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a301"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a302"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">if&nbsp;</span><span class="src-sym">(</span><span class="src-var">$wantv</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a303"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$i&nbsp;</span>=&nbsp;<span class="src-num">0</span><span class="src-sym">;&nbsp;</span><span class="src-var">$i&nbsp;</span>&lt;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">n</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$i</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a304"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$t&nbsp;</span>=&nbsp;<span class="src-var">$cs&nbsp;</span>*&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">V</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]&nbsp;</span>+&nbsp;<span class="src-var">$sn&nbsp;</span>*&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">V</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$p</span>-<span class="src-num">1</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a305"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">V</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$p</span>-<span class="src-num">1</span><span class="src-sym">]&nbsp;</span>=&nbsp;-<span class="src-var">$sn&nbsp;</span>*&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">V</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]&nbsp;</span>+&nbsp;<span class="src-var">$cs&nbsp;</span>*&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">V</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$p</span>-<span class="src-num">1</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a306"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">V</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-var">$t</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a307"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a308"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a309"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a310"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">break</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a311"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;Split&nbsp;at&nbsp;negligible&nbsp;s(k).</span></div></li>
<li><div class="src-line"><a name="a312"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">case&nbsp;</span><span class="src-num">2</span>:</div></li>
<li><div class="src-line"><a name="a313"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$f&nbsp;</span>=&nbsp;<span class="src-var">$e</span><span class="src-sym">[</span><span class="src-var">$k</span>-<span class="src-num">1</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a314"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$e</span><span class="src-sym">[</span><span class="src-var">$k</span>-<span class="src-num">1</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-num">0.0</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a315"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$j&nbsp;</span>=&nbsp;<span class="src-var">$k</span><span class="src-sym">;&nbsp;</span><span class="src-var">$j&nbsp;</span>&lt;&nbsp;<span class="src-var">$p</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$j</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a316"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$t&nbsp;</span>=&nbsp;<a href="../JAMA/_PHPExcel---Shared---JAMA---utils---Maths.php.html#functionhypo">hypo</a><span class="src-sym">(</span><span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">s</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]</span><span class="src-sym">,&nbsp;</span><span class="src-var">$f</span><span class="src-sym">)</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a317"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$cs&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">s</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]&nbsp;</span>/&nbsp;<span class="src-var">$t</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a318"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$sn&nbsp;</span>=&nbsp;<span class="src-var">$f&nbsp;</span>/&nbsp;<span class="src-var">$t</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a319"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">s</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-var">$t</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a320"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$f&nbsp;</span>=&nbsp;-<span class="src-var">$sn&nbsp;</span>*&nbsp;<span class="src-var">$e</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a321"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$e</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-var">$cs&nbsp;</span>*&nbsp;<span class="src-var">$e</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a322"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">if&nbsp;</span><span class="src-sym">(</span><span class="src-var">$wantu</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a323"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$i&nbsp;</span>=&nbsp;<span class="src-num">0</span><span class="src-sym">;&nbsp;</span><span class="src-var">$i&nbsp;</span>&lt;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">m</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$i</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a324"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$t&nbsp;</span>=&nbsp;<span class="src-var">$cs&nbsp;</span>*&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">U</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]&nbsp;</span>+&nbsp;<span class="src-var">$sn&nbsp;</span>*&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">U</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$k</span>-<span class="src-num">1</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a325"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">U</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$k</span>-<span class="src-num">1</span><span class="src-sym">]&nbsp;</span>=&nbsp;-<span class="src-var">$sn&nbsp;</span>*&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">U</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]&nbsp;</span>+&nbsp;<span class="src-var">$cs&nbsp;</span>*&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">U</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$k</span>-<span class="src-num">1</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a326"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">U</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-var">$t</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a327"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a328"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a329"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a330"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">break</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a331"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;Perform&nbsp;one&nbsp;qr&nbsp;step.</span></div></li>
<li><div class="src-line"><a name="a332"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">case&nbsp;</span><span class="src-num">3</span>:</div></li>
<li><div class="src-line"><a name="a333"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;Calculate&nbsp;the&nbsp;shift.</span></div></li>
<li><div class="src-line"><a name="a334"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$scale&nbsp;</span>=&nbsp;<a href="http://www.php.net/max">max</a><span class="src-sym">(</span><a href="http://www.php.net/max">max</a><span class="src-sym">(</span><a href="http://www.php.net/max">max</a><span class="src-sym">(</span><a href="http://www.php.net/max">max</a><span class="src-sym">(</span></div></li>
<li><div class="src-line"><a name="a335"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<a href="http://www.php.net/abs">abs</a><span class="src-sym">(</span><span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">s</span><span class="src-sym">[</span><span class="src-var">$p</span>-<span class="src-num">1</span><span class="src-sym">]</span><span class="src-sym">)</span><span class="src-sym">,</span><a href="http://www.php.net/abs">abs</a><span class="src-sym">(</span><span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">s</span><span class="src-sym">[</span><span class="src-var">$p</span>-<span class="src-num">2</span><span class="src-sym">]</span><span class="src-sym">))</span><span class="src-sym">,</span><a href="http://www.php.net/abs">abs</a><span class="src-sym">(</span><span class="src-var">$e</span><span class="src-sym">[</span><span class="src-var">$p</span>-<span class="src-num">2</span><span class="src-sym">]</span><span class="src-sym">))</span><span class="src-sym">,</span></div></li>
<li><div class="src-line"><a name="a336"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<a href="http://www.php.net/abs">abs</a><span class="src-sym">(</span><span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">s</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]</span><span class="src-sym">))</span><span class="src-sym">,&nbsp;</span><a href="http://www.php.net/abs">abs</a><span class="src-sym">(</span><span class="src-var">$e</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]</span><span class="src-sym">))</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a337"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$sp&nbsp;&nbsp;&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">s</span><span class="src-sym">[</span><span class="src-var">$p</span>-<span class="src-num">1</span><span class="src-sym">]&nbsp;</span>/&nbsp;<span class="src-var">$scale</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a338"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$spm1&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">s</span><span class="src-sym">[</span><span class="src-var">$p</span>-<span class="src-num">2</span><span class="src-sym">]&nbsp;</span>/&nbsp;<span class="src-var">$scale</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a339"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$epm1&nbsp;</span>=&nbsp;<span class="src-var">$e</span><span class="src-sym">[</span><span class="src-var">$p</span>-<span class="src-num">2</span><span class="src-sym">]&nbsp;</span>/&nbsp;<span class="src-var">$scale</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a340"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$sk&nbsp;&nbsp;&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">s</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]&nbsp;</span>/&nbsp;<span class="src-var">$scale</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a341"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$ek&nbsp;&nbsp;&nbsp;</span>=&nbsp;<span class="src-var">$e</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]&nbsp;</span>/&nbsp;<span class="src-var">$scale</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a342"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$b&nbsp;&nbsp;&nbsp;&nbsp;</span>=&nbsp;<span class="src-sym">((</span><span class="src-var">$spm1&nbsp;</span>+&nbsp;<span class="src-var">$sp</span><span class="src-sym">)&nbsp;</span>*&nbsp;<span class="src-sym">(</span><span class="src-var">$spm1&nbsp;</span>-&nbsp;<span class="src-var">$sp</span><span class="src-sym">)&nbsp;</span>+&nbsp;<span class="src-var">$epm1&nbsp;</span>*&nbsp;<span class="src-var">$epm1</span><span class="src-sym">)&nbsp;</span>/&nbsp;<span class="src-num">2.0</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a343"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$c&nbsp;&nbsp;&nbsp;&nbsp;</span>=&nbsp;<span class="src-sym">(</span><span class="src-var">$sp&nbsp;</span>*&nbsp;<span class="src-var">$epm1</span><span class="src-sym">)&nbsp;</span>*&nbsp;<span class="src-sym">(</span><span class="src-var">$sp&nbsp;</span>*&nbsp;<span class="src-var">$epm1</span><span class="src-sym">)</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a344"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$shift&nbsp;</span>=&nbsp;<span class="src-num">0.0</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a345"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">if&nbsp;</span><span class="src-sym">((</span><span class="src-var">$b&nbsp;</span>!=&nbsp;<span class="src-num">0.0</span><span class="src-sym">)&nbsp;</span>||&nbsp;<span class="src-sym">(</span><span class="src-var">$c&nbsp;</span>!=&nbsp;<span class="src-num">0.0</span><span class="src-sym">))&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a346"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$shift&nbsp;</span>=&nbsp;<a href="http://www.php.net/sqrt">sqrt</a><span class="src-sym">(</span><span class="src-var">$b&nbsp;</span>*&nbsp;<span class="src-var">$b&nbsp;</span>+&nbsp;<span class="src-var">$c</span><span class="src-sym">)</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a347"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">if&nbsp;</span><span class="src-sym">(</span><span class="src-var">$b&nbsp;</span>&lt;&nbsp;<span class="src-num">0.0</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a348"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$shift&nbsp;</span>=&nbsp;-<span class="src-var">$shift</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a349"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a350"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$shift&nbsp;</span>=&nbsp;<span class="src-var">$c&nbsp;</span>/&nbsp;<span class="src-sym">(</span><span class="src-var">$b&nbsp;</span>+&nbsp;<span class="src-var">$shift</span><span class="src-sym">)</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a351"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a352"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$f&nbsp;</span>=&nbsp;<span class="src-sym">(</span><span class="src-var">$sk&nbsp;</span>+&nbsp;<span class="src-var">$sp</span><span class="src-sym">)&nbsp;</span>*&nbsp;<span class="src-sym">(</span><span class="src-var">$sk&nbsp;</span>-&nbsp;<span class="src-var">$sp</span><span class="src-sym">)&nbsp;</span>+&nbsp;<span class="src-var">$shift</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a353"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$g&nbsp;</span>=&nbsp;<span class="src-var">$sk&nbsp;</span>*&nbsp;<span class="src-var">$ek</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a354"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;Chase&nbsp;zeros.</span></div></li>
<li><div class="src-line"><a name="a355"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$j&nbsp;</span>=&nbsp;<span class="src-var">$k</span><span class="src-sym">;&nbsp;</span><span class="src-var">$j&nbsp;</span>&lt;&nbsp;<span class="src-var">$p</span>-<span class="src-num">1</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$j</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a356"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$t&nbsp;&nbsp;</span>=&nbsp;<a href="../JAMA/_PHPExcel---Shared---JAMA---utils---Maths.php.html#functionhypo">hypo</a><span class="src-sym">(</span><span class="src-var">$f</span><span class="src-sym">,</span><span class="src-var">$g</span><span class="src-sym">)</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a357"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$cs&nbsp;</span>=&nbsp;<span class="src-var">$f</span>/<span class="src-var">$t</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a358"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$sn&nbsp;</span>=&nbsp;<span class="src-var">$g</span>/<span class="src-var">$t</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a359"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">if&nbsp;</span><span class="src-sym">(</span><span class="src-var">$j&nbsp;</span>!=&nbsp;<span class="src-var">$k</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a360"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$e</span><span class="src-sym">[</span><span class="src-var">$j</span>-<span class="src-num">1</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-var">$t</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a361"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a362"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$f&nbsp;</span>=&nbsp;<span class="src-var">$cs&nbsp;</span>*&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">s</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]&nbsp;</span>+&nbsp;<span class="src-var">$sn&nbsp;</span>*&nbsp;<span class="src-var">$e</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a363"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$e</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-var">$cs&nbsp;</span>*&nbsp;<span class="src-var">$e</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]&nbsp;</span>-&nbsp;<span class="src-var">$sn&nbsp;</span>*&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">s</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a364"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$g&nbsp;</span>=&nbsp;<span class="src-var">$sn&nbsp;</span>*&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">s</span><span class="src-sym">[</span><span class="src-var">$j</span>+<span class="src-num">1</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a365"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">s</span><span class="src-sym">[</span><span class="src-var">$j</span>+<span class="src-num">1</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-var">$cs&nbsp;</span>*&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">s</span><span class="src-sym">[</span><span class="src-var">$j</span>+<span class="src-num">1</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a366"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">if&nbsp;</span><span class="src-sym">(</span><span class="src-var">$wantv</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a367"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$i&nbsp;</span>=&nbsp;<span class="src-num">0</span><span class="src-sym">;&nbsp;</span><span class="src-var">$i&nbsp;</span>&lt;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">n</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$i</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a368"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$t&nbsp;</span>=&nbsp;<span class="src-var">$cs&nbsp;</span>*&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">V</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]&nbsp;</span>+&nbsp;<span class="src-var">$sn&nbsp;</span>*&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">V</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$j</span>+<span class="src-num">1</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a369"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">V</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$j</span>+<span class="src-num">1</span><span class="src-sym">]&nbsp;</span>=&nbsp;-<span class="src-var">$sn&nbsp;</span>*&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">V</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]&nbsp;</span>+&nbsp;<span class="src-var">$cs&nbsp;</span>*&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">V</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$j</span>+<span class="src-num">1</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a370"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">V</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-var">$t</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a371"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a372"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a373"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$t&nbsp;</span>=&nbsp;<a href="../JAMA/_PHPExcel---Shared---JAMA---utils---Maths.php.html#functionhypo">hypo</a><span class="src-sym">(</span><span class="src-var">$f</span><span class="src-sym">,</span><span class="src-var">$g</span><span class="src-sym">)</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a374"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$cs&nbsp;</span>=&nbsp;<span class="src-var">$f</span>/<span class="src-var">$t</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a375"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$sn&nbsp;</span>=&nbsp;<span class="src-var">$g</span>/<span class="src-var">$t</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a376"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">s</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-var">$t</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a377"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$f&nbsp;</span>=&nbsp;<span class="src-var">$cs&nbsp;</span>*&nbsp;<span class="src-var">$e</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]&nbsp;</span>+&nbsp;<span class="src-var">$sn&nbsp;</span>*&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">s</span><span class="src-sym">[</span><span class="src-var">$j</span>+<span class="src-num">1</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a378"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">s</span><span class="src-sym">[</span><span class="src-var">$j</span>+<span class="src-num">1</span><span class="src-sym">]&nbsp;</span>=&nbsp;-<span class="src-var">$sn&nbsp;</span>*&nbsp;<span class="src-var">$e</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]&nbsp;</span>+&nbsp;<span class="src-var">$cs&nbsp;</span>*&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">s</span><span class="src-sym">[</span><span class="src-var">$j</span>+<span class="src-num">1</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a379"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$g&nbsp;</span>=&nbsp;<span class="src-var">$sn&nbsp;</span>*&nbsp;<span class="src-var">$e</span><span class="src-sym">[</span><span class="src-var">$j</span>+<span class="src-num">1</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a380"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$e</span><span class="src-sym">[</span><span class="src-var">$j</span>+<span class="src-num">1</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-var">$cs&nbsp;</span>*&nbsp;<span class="src-var">$e</span><span class="src-sym">[</span><span class="src-var">$j</span>+<span class="src-num">1</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a381"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">if&nbsp;</span><span class="src-sym">(</span><span class="src-var">$wantu&nbsp;</span>&amp;&amp;&nbsp;<span class="src-sym">(</span><span class="src-var">$j&nbsp;</span>&lt;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">m&nbsp;</span>-&nbsp;<span class="src-num">1</span><span class="src-sym">))&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a382"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$i&nbsp;</span>=&nbsp;<span class="src-num">0</span><span class="src-sym">;&nbsp;</span><span class="src-var">$i&nbsp;</span>&lt;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">m</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$i</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a383"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$t&nbsp;</span>=&nbsp;<span class="src-var">$cs&nbsp;</span>*&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">U</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]&nbsp;</span>+&nbsp;<span class="src-var">$sn&nbsp;</span>*&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">U</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$j</span>+<span class="src-num">1</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a384"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">U</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$j</span>+<span class="src-num">1</span><span class="src-sym">]&nbsp;</span>=&nbsp;-<span class="src-var">$sn&nbsp;</span>*&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">U</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]&nbsp;</span>+&nbsp;<span class="src-var">$cs&nbsp;</span>*&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">U</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$j</span>+<span class="src-num">1</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a385"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">U</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-var">$t</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a386"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a387"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a388"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a389"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$e</span><span class="src-sym">[</span><span class="src-var">$p</span>-<span class="src-num">2</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-var">$f</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a390"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$iter&nbsp;</span>=&nbsp;<span class="src-var">$iter&nbsp;</span>+&nbsp;<span class="src-num">1</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a391"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">break</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a392"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;Convergence.</span></div></li>
<li><div class="src-line"><a name="a393"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">case&nbsp;</span><span class="src-num">4</span>:</div></li>
<li><div class="src-line"><a name="a394"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;Make&nbsp;the&nbsp;singular&nbsp;values&nbsp;positive.</span></div></li>
<li><div class="src-line"><a name="a395"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">if&nbsp;</span><span class="src-sym">(</span><span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">s</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]&nbsp;</span>&lt;=&nbsp;<span class="src-num">0.0</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a396"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">s</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-sym">(</span><span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">s</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]&nbsp;</span>&lt;&nbsp;<span class="src-num">0.0&nbsp;</span>?&nbsp;-<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">s</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]&nbsp;</span>:&nbsp;<span class="src-num">0.0</span><span class="src-sym">)</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a397"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">if&nbsp;</span><span class="src-sym">(</span><span class="src-var">$wantv</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a398"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$i&nbsp;</span>=&nbsp;<span class="src-num">0</span><span class="src-sym">;&nbsp;</span><span class="src-var">$i&nbsp;</span>&lt;=&nbsp;<span class="src-var">$pp</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$i</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a399"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">V</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]&nbsp;</span>=&nbsp;-<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">V</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a400"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a401"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a402"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a403"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;Order&nbsp;the&nbsp;singular&nbsp;values.</span></div></li>
<li><div class="src-line"><a name="a404"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">while&nbsp;</span><span class="src-sym">(</span><span class="src-var">$k&nbsp;</span>&lt;&nbsp;<span class="src-var">$pp</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a405"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">if&nbsp;</span><span class="src-sym">(</span><span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">s</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]&nbsp;</span>&gt;=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">s</span><span class="src-sym">[</span><span class="src-var">$k</span>+<span class="src-num">1</span><span class="src-sym">]</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a406"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">break</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a407"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a408"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$t&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">s</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a409"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">s</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">s</span><span class="src-sym">[</span><span class="src-var">$k</span>+<span class="src-num">1</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a410"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">s</span><span class="src-sym">[</span><span class="src-var">$k</span>+<span class="src-num">1</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-var">$t</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a411"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">if&nbsp;</span><span class="src-sym">(</span><span class="src-var">$wantv&nbsp;</span><span class="src-key">AND&nbsp;</span><span class="src-sym">(</span><span class="src-var">$k&nbsp;</span>&lt;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">n&nbsp;</span>-&nbsp;<span class="src-num">1</span><span class="src-sym">))&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a412"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$i&nbsp;</span>=&nbsp;<span class="src-num">0</span><span class="src-sym">;&nbsp;</span><span class="src-var">$i&nbsp;</span>&lt;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">n</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$i</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a413"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$t&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">V</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$k</span>+<span class="src-num">1</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a414"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">V</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$k</span>+<span class="src-num">1</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">V</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a415"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">V</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-var">$t</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a416"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a417"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a418"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">if&nbsp;</span><span class="src-sym">(</span><span class="src-var">$wantu&nbsp;</span><span class="src-key">AND&nbsp;</span><span class="src-sym">(</span><span class="src-var">$k&nbsp;</span>&lt;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">m</span>-<span class="src-num">1</span><span class="src-sym">))&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a419"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$i&nbsp;</span>=&nbsp;<span class="src-num">0</span><span class="src-sym">;&nbsp;</span><span class="src-var">$i&nbsp;</span>&lt;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">m</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$i</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a420"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$t&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">U</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$k</span>+<span class="src-num">1</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a421"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">U</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$k</span>+<span class="src-num">1</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">U</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a422"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">U</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-var">$t</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a423"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a424"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a425"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;++<span class="src-var">$k</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a426"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a427"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$iter&nbsp;</span>=&nbsp;<span class="src-num">0</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a428"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;--<span class="src-var">$p</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a429"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">break</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a430"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}&nbsp;</span><span class="src-comm">//&nbsp;end&nbsp;switch</span></div></li>
<li><div class="src-line"><a name="a431"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}&nbsp;</span><span class="src-comm">//&nbsp;end&nbsp;while</span></div></li>
<li><div class="src-line"><a name="a432"></a>&nbsp;</div></li>
<li><div class="src-line"><a name="a433"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}&nbsp;</span><span class="src-comm">//&nbsp;end&nbsp;constructor</span></div></li>
<li><div class="src-line"><a name="a434"></a>&nbsp;</div></li>
<li><div class="src-line"><a name="a435"></a>&nbsp;</div></li>
<li><div class="src-line"><a name="a436"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-doc">/**</span></div></li>
<li><div class="src-line"><a name="a437"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;Return&nbsp;the&nbsp;left&nbsp;singular&nbsp;vectors</span></div></li>
<li><div class="src-line"><a name="a438"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*</span></div></li>
<li><div class="src-line"><a name="a439"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;</span><span class="src-doc-coretag">@access</span><span class="src-doc">&nbsp;public</span></div></li>
<li><div class="src-line"><a name="a440"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;</span><span class="src-doc-coretag">@return&nbsp;</span><span class="src-doc-type">U&nbsp;</span></div></li>
<li><div class="src-line"><a name="a441"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*/</span></div></li>
<li><div class="src-line"><a name="a442"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">public&nbsp;</span><span class="src-key">function&nbsp;</span><a href="../JAMA/SingularValueDecomposition.html#methodgetU">getU</a><span class="src-sym">(</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a443"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">return&nbsp;</span><span class="src-key">new&nbsp;</span><span class="src-id">Matrix</span><span class="src-sym">(</span><span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">U</span><span class="src-sym">,&nbsp;</span><span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">m</span><span class="src-sym">,&nbsp;</span><a href="http://www.php.net/min">min</a><span class="src-sym">(</span><span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">m&nbsp;</span>+&nbsp;<span class="src-num">1</span><span class="src-sym">,&nbsp;</span><span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">n</span><span class="src-sym">))</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a444"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a445"></a>&nbsp;</div></li>
<li><div class="src-line"><a name="a446"></a>&nbsp;</div></li>
<li><div class="src-line"><a name="a447"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-doc">/**</span></div></li>
<li><div class="src-line"><a name="a448"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;Return&nbsp;the&nbsp;right&nbsp;singular&nbsp;vectors</span></div></li>
<li><div class="src-line"><a name="a449"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*</span></div></li>
<li><div class="src-line"><a name="a450"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;</span><span class="src-doc-coretag">@access</span><span class="src-doc">&nbsp;public</span></div></li>
<li><div class="src-line"><a name="a451"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;</span><span class="src-doc-coretag">@return&nbsp;</span><span class="src-doc-type">V&nbsp;</span></div></li>
<li><div class="src-line"><a name="a452"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*/</span></div></li>
<li><div class="src-line"><a name="a453"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">public&nbsp;</span><span class="src-key">function&nbsp;</span><a href="../JAMA/SingularValueDecomposition.html#methodgetV">getV</a><span class="src-sym">(</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a454"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">return&nbsp;</span><span class="src-key">new&nbsp;</span><span class="src-id">Matrix</span><span class="src-sym">(</span><span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">V</span><span class="src-sym">)</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a455"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a456"></a>&nbsp;</div></li>
<li><div class="src-line"><a name="a457"></a>&nbsp;</div></li>
<li><div class="src-line"><a name="a458"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-doc">/**</span></div></li>
<li><div class="src-line"><a name="a459"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;Return&nbsp;the&nbsp;one-dimensional&nbsp;array&nbsp;of&nbsp;singular&nbsp;values</span></div></li>
<li><div class="src-line"><a name="a460"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*</span></div></li>
<li><div class="src-line"><a name="a461"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;</span><span class="src-doc-coretag">@access</span><span class="src-doc">&nbsp;public</span></div></li>
<li><div class="src-line"><a name="a462"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;</span><span class="src-doc-coretag">@return&nbsp;</span><span class="src-doc-type">diagonal&nbsp;</span><span class="src-doc">of&nbsp;S.</span></div></li>
<li><div class="src-line"><a name="a463"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*/</span></div></li>
<li><div class="src-line"><a name="a464"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">public&nbsp;</span><span class="src-key">function&nbsp;</span><a href="../JAMA/SingularValueDecomposition.html#methodgetSingularValues">getSingularValues</a><span class="src-sym">(</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a465"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">return&nbsp;</span><span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">s</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a466"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a467"></a>&nbsp;</div></li>
<li><div class="src-line"><a name="a468"></a>&nbsp;</div></li>
<li><div class="src-line"><a name="a469"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-doc">/**</span></div></li>
<li><div class="src-line"><a name="a470"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;Return&nbsp;the&nbsp;diagonal&nbsp;matrix&nbsp;of&nbsp;singular&nbsp;values</span></div></li>
<li><div class="src-line"><a name="a471"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*</span></div></li>
<li><div class="src-line"><a name="a472"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;</span><span class="src-doc-coretag">@access</span><span class="src-doc">&nbsp;public</span></div></li>
<li><div class="src-line"><a name="a473"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;</span><span class="src-doc-coretag">@return&nbsp;</span><span class="src-doc-type">S&nbsp;</span></div></li>
<li><div class="src-line"><a name="a474"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*/</span></div></li>
<li><div class="src-line"><a name="a475"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">public&nbsp;</span><span class="src-key">function&nbsp;</span><a href="../JAMA/SingularValueDecomposition.html#methodgetS">getS</a><span class="src-sym">(</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a476"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$i&nbsp;</span>=&nbsp;<span class="src-num">0</span><span class="src-sym">;&nbsp;</span><span class="src-var">$i&nbsp;</span>&lt;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">n</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$i</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a477"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$j&nbsp;</span>=&nbsp;<span class="src-num">0</span><span class="src-sym">;&nbsp;</span><span class="src-var">$j&nbsp;</span>&lt;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">n</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$j</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a478"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$S</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-num">0.0</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a479"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a480"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$S</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">s</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a481"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a482"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">return&nbsp;</span><span class="src-key">new&nbsp;</span><span class="src-id">Matrix</span><span class="src-sym">(</span><span class="src-var">$S</span><span class="src-sym">)</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a483"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a484"></a>&nbsp;</div></li>
<li><div class="src-line"><a name="a485"></a>&nbsp;</div></li>
<li><div class="src-line"><a name="a486"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-doc">/**</span></div></li>
<li><div class="src-line"><a name="a487"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;Two&nbsp;norm</span></div></li>
<li><div class="src-line"><a name="a488"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*</span></div></li>
<li><div class="src-line"><a name="a489"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;</span><span class="src-doc-coretag">@access</span><span class="src-doc">&nbsp;public</span></div></li>
<li><div class="src-line"><a name="a490"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;</span><span class="src-doc-coretag">@return&nbsp;</span><span class="src-doc-type">max(S)&nbsp;</span></div></li>
<li><div class="src-line"><a name="a491"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*/</span></div></li>
<li><div class="src-line"><a name="a492"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">public&nbsp;</span><span class="src-key">function&nbsp;</span><a href="../JAMA/SingularValueDecomposition.html#methodnorm2">norm2</a><span class="src-sym">(</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a493"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">return&nbsp;</span><span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">s</span><span class="src-sym">[</span><span class="src-num">0</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a494"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a495"></a>&nbsp;</div></li>
<li><div class="src-line"><a name="a496"></a>&nbsp;</div></li>
<li><div class="src-line"><a name="a497"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-doc">/**</span></div></li>
<li><div class="src-line"><a name="a498"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;Two&nbsp;norm&nbsp;condition&nbsp;number</span></div></li>
<li><div class="src-line"><a name="a499"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*</span></div></li>
<li><div class="src-line"><a name="a500"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;</span><span class="src-doc-coretag">@access</span><span class="src-doc">&nbsp;public</span></div></li>
<li><div class="src-line"><a name="a501"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;</span><span class="src-doc-coretag">@return&nbsp;</span><span class="src-doc-type">max(S)/min(S)&nbsp;</span></div></li>
<li><div class="src-line"><a name="a502"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*/</span></div></li>
<li><div class="src-line"><a name="a503"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">public&nbsp;</span><span class="src-key">function&nbsp;</span><a href="../JAMA/SingularValueDecomposition.html#methodcond">cond</a><span class="src-sym">(</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a504"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">return&nbsp;</span><span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">s</span><span class="src-sym">[</span><span class="src-num">0</span><span class="src-sym">]&nbsp;</span>/&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">s</span><span class="src-sym">[</span><a href="http://www.php.net/min">min</a><span class="src-sym">(</span><span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">m</span><span class="src-sym">,&nbsp;</span><span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">n</span><span class="src-sym">)&nbsp;</span>-&nbsp;<span class="src-num">1</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a505"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a506"></a>&nbsp;</div></li>
<li><div class="src-line"><a name="a507"></a>&nbsp;</div></li>
<li><div class="src-line"><a name="a508"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-doc">/**</span></div></li>
<li><div class="src-line"><a name="a509"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;Effective&nbsp;numerical&nbsp;matrix&nbsp;rank</span></div></li>
<li><div class="src-line"><a name="a510"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*</span></div></li>
<li><div class="src-line"><a name="a511"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;</span><span class="src-doc-coretag">@access</span><span class="src-doc">&nbsp;public</span></div></li>
<li><div class="src-line"><a name="a512"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;</span><span class="src-doc-coretag">@return&nbsp;</span><span class="src-doc-type">Number&nbsp;</span><span class="src-doc">of&nbsp;nonnegligible&nbsp;singular&nbsp;values.</span></div></li>
<li><div class="src-line"><a name="a513"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*/</span></div></li>
<li><div class="src-line"><a name="a514"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">public&nbsp;</span><span class="src-key">function&nbsp;</span><a href="../JAMA/SingularValueDecomposition.html#methodrank">rank</a><span class="src-sym">(</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a515"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$eps&nbsp;</span>=&nbsp;<a href="http://www.php.net/pow">pow</a><span class="src-sym">(</span><span class="src-num">2.0</span><span class="src-sym">,&nbsp;</span>-<span class="src-num">52.0</span><span class="src-sym">)</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a516"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$tol&nbsp;</span>=&nbsp;<a href="http://www.php.net/max">max</a><span class="src-sym">(</span><span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">m</span><span class="src-sym">,&nbsp;</span><span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">n</span><span class="src-sym">)&nbsp;</span>*&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">s</span><span class="src-sym">[</span><span class="src-num">0</span><span class="src-sym">]&nbsp;</span>*&nbsp;<span class="src-var">$eps</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a517"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$r&nbsp;</span>=&nbsp;<span class="src-num">0</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a518"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$i&nbsp;</span>=&nbsp;<span class="src-num">0</span><span class="src-sym">;&nbsp;</span><span class="src-var">$i&nbsp;</span>&lt;&nbsp;<a href="http://www.php.net/count">count</a><span class="src-sym">(</span><span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">s</span><span class="src-sym">)</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$i</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a519"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">if&nbsp;</span><span class="src-sym">(</span><span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">s</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]&nbsp;</span>&gt;&nbsp;<span class="src-var">$tol</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a520"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;++<span class="src-var">$r</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a521"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a522"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a523"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">return&nbsp;</span><span class="src-var">$r</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a524"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a525"></a>&nbsp;</div></li>
<li><div class="src-line"><a name="a526"></a><span class="src-sym">}&nbsp;&nbsp;&nbsp;&nbsp;</span><span class="src-comm">//&nbsp;&nbsp;&nbsp;&nbsp;class&nbsp;SingularValueDecomposition</span></div></li>
</ol>
</div>
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		    Documentation generated on Fri, 12 Oct 2012 00:17:45 +0200 by <a href="http://www.phpdoc.org">phpDocumentor 1.4.4</a>
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